1.
2.
Solution:
1)
Use factoring,
x^2(4x^2 - 18) = 0, using ZFT
x^2 = 0, that means a double root of zero, {0 ,0}and next is 4x^2 - 18 = 0,
for 4x^2 - 18 = 0
x^2 = 18/4
x1 = (3/2) sqrt 2
x2 = -(3/2) sqrt 2
x = {0, 0, (3/2) sqrt 2, x2 = -(3/2) sqrt 2}
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2)
,
(3x + 1)^(1/3) = 5,
raise to 3 both sides
[(3x + 1)^(1/3)]^3 = [5]^3,
3x + 1 = 125, solving for x, we have
3x = 125 - 1,
3x = 124
x = 124/3 = 41.333333 . . . .
CHECK: (3(124/3) + 1)^1/3 - 5 = 0,
(124 + 1)^1/3 - 5 = 0
125^1/3 - 5 = 0
5 - 5 = 0
0 = 0, indeed
see graph